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The Hubbard model describes the physics of strongly correlated electron systems, but is difficult to solve. Now, a scheme to systematically and efficiently relate the exactly solvable Hatsugai–Kohmoto model to the Hubbard model has been identified.

High-temperature behaviour of thermopower is special in cuprates, allowing for theory-experiment comparisons. Wang et al. use quantum Monte Carlo to compute high temperature thermopower in the Hubbard model, demonstrating qualitative and quantitative agreement with experiments across multiple cuprate families.

A several-fold reduction in temperature is accomplished using a neutral-atom Hubbard quantum simulator by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters.

Confining semiconductor dipolar excitons using an artificial two-dimensional square lattice emulates extended Bose–Hubbard Hamiltonians, thus enabling control of boson-like arrays in lattices with programmable geometries and more than 100 sites.

A technique analogous to angle-resolved photoemission spectroscopy used in materials characterization has been developed for interacting Fermi gases in an optical lattice, providing information on the single-particle excitations in a many-body system.

A quantum simulation platform based on quantum dots is reported that can operate at relatively low temperatures, and its utility is shown by simulating a Fermi–Hubbard model.

Recent experiments have identified the underlying model of one-dimensional cuprate chains as the extended Hubbard model with attractive near-neighbor interactions. Here, the authors use many-body calculations to create an exact ground-state phase diagram of this model, demonstrating a rich diversity of exotic quantum states, and providing valuable guidance for realizing unconventional superconductivity in the system.

Three-dimensional (3D) strongly correlated many-body systems and their dynamics across quantum phase transitions pose a challenge when it comes to numerical simulations. The authors experimentally demonstrated that such many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, and observed dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions.

Moire bilayers support quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states, but a unified explanation is missing. Mai et al. show that by including interactions in typical models, the QSH state shifts from 1/2 to 1/4 filling and gives way to the QAH state at low temperature.

The optimal condition for superconductivity is a long-sought issue but remains challenging. Here, Ivashko et al. demonstrate that the compressive strain to La₂CuO₄ films enhances the Coulomb and magnetic-exchange interactions relevant for superconductivity, providing a strategy to optimise the parent Mott state for superconductivity.

A large-scale study on the replicability of claims from social and behavioural science journals reports that about half of the results replicate in the same patterns as the original study.

The Mott insulator ground state is a crucial feature of high-temperature superconductors such as the cuprates. Here, the authors find an exactly solvable model that contains both superconductivity and Mottness.

Gene correction in the lung is achieved with inhalable mRNA lipid nanoparticles containing an amino acid-derived ionizable lipid identified from screening and structure–function optimization studies.

A Mott insulator forms when strong interactions between particles cause them to become localized. A cold atom simulator has now been used to realize a selective Mott insulator in which atoms are localized or propagating depending on their spin state.

Spintronics, graphene, and carbon nanotubes are potential components of next-generation high performance computers. Here, the authors propose and theoretically evaluate a spintronic logic family composed solely of carbon materials with the potential for a 100 × improvement in energy efficiency.

The Hofstadter–Hubbard model on 2D square lattices is a paradigmatic model to study the interplay of electron correlations and external magnetic field. The authors use quantum Monte Carlo to study the thermodynamic properties of the Hofstadter Hamiltonian at intermediate to strong coupling, finding that a strong orbital magnetic field delocalizes electrons and reduces the effective Hubbard interaction.

An outstanding question about the iron-based superconductors has been whether or not their magnetic characteristics are dominated by itinerant or localized magnetic moments. Absolute measurements and calculations of the magnetic response of undoped and Ni-doped BaFe₂As₂ indicate the latter.

Quantifying the degree of correlation required to drive a Mott insulator transition is a crucial aspect in understanding and manipulating correlated electrons. Here, the authors introduce a thallium-based cuprate system and use resonant inelastic X-ray scattering, combined with Hubbard-Heisenberg modeling, to establish a universal relation between electron interactions and magnon dispersion, suggesting optimal superconductivity at intermediate correlation strength.

The Mott metal-to-insulator transition plays a key role in theoretical studies of high-temperature superconductors. A mathematical analysis of the theory of metals identifies a renormalization-group fixed point describing Mott physics.

To simulate physical systems on a quantum computer, their degrees of freedom must be encoded into qubits. This Review assesses the different methods that exist to allow quantum calculation of fermionic systems.

The authors demonstrate a method controlling the lattice filling of doped 1D Bose-Hubbard system of Rb atoms composed of chains of 3 to 6 sites in an optical lattice. The control is achieved by changing of the light potential and interaction strength.

The influence of spin–orbit coupling on itinerant electrons underlies the formation of spin–orbit Mott states. Here, the authors demonstrate a temperature-hysteretic cascade between charge-ordered phases stabilized by localized 5dspin–orbit Mott dimer states in metallic iridium ditelluride.

The emergence of quasiparticles in a doped Mott insulator is the key to understanding high Tc cuprate superconductivity - a major quest in condensed matter physics. Here, the authors investigate the angle-resolved photoemission spectroscopy in the cuprates and observe how the quasiparticle emerges from the Mott insulating regime.

Quantum geometry captures how electronic wavefunctions delocalize across crystal lattices, introducing length and energy scales beyond band dispersion. This Perspective shows how these hidden scales shape material properties, from dielectric response and optical absorption to the robustness of superconductivity and other emergent phases.

1T-TaS2 possesses complex electronic phase behaviors in transition-metal di-chalcogenides, undergoing several charge-ordered phases before finally into an insulating state of unknown origin. Here, the authors determine its electronic and structural properties experimentally, revealing its origin.

The integration of strong electron correlations into topological systems is advancing the exploration of topological materials. Here, abnormal Mott physics emerges in weakly correlated 4f fermions through their interplay with topological singularity.

The origin of bad-metal resistivity is a long-standing problem for condensed matter physics. Here the authors show anomalous resistivity, transport lifetime, and relaxation dynamics consistent with bad-metal behavior over a wide range of temperature for fermionic potassium atoms in optical lattices.

Chiral spin liquids, a topological phase in frustrated quantum spin systems, have been recently very sought-after. Here, Bauer et al.present a model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry exhibiting such a topological phase.

An Fe^III/V redox mechanism in Li₄FeSbO₆ on delithiation without Fe^IV or oxygen formation with resistance to aging, high operating potential and low voltage hysteresis is demonstrated, with implications for Fe-based high-voltage applications.

Adatoms on the surface of silicon can create two-dimensional superconductivity, the order parameter symmetry of which is currently not known. Now, evidence suggests it might be a topological chiral d-wave state.

The influence of surface ponding on the interior of ice shelves is currently unknown. Here, the authors combine surface and borehole geophysics on the Larsen C Ice Shelf, Antarctica, with remote sensing and modelling and show how pond refreezing increases ice shelf density and temperature.

Previous understanding of the coupling between ferroelectric structure and magnetic texture in BiFeO₃ has relied on mesoscale measurements. Here, the authors image coupling directly, showing a complex spin cycloid controlled with electric field.